The estimation of the shape of an array using a hidden Markov model

A hidden Markov model (HMM) technique for the estimation of the shape of a towed array is presented. It is assumed that there is a far-field source radiating sound containing possibly weak spectral lines. The technique uses either the Fourier coefficients at a given frequency computed from a single time block or the maximal eigenvector of a sample spectral covariance matrix. The technique is illustrated using several simulations. The results of these simulations indicate that the HMM technique yields shape and bearing estimates more accurate than those provided by a maximum-likelihood array shape estimation technique     

Double-diffusive convection with a non-linear equation of state: Part I. The accurate conservation of properties in a two-layer system

If the equation of state is nonlinear, a given flux of heat across a double diffusive interface causes different buoyancy fluxes in the upper and lower layers. This results in different convective activity in the two layers and can lead to preferential entrainment across the interface in one direction (i.e. a migration of the interface). In this paper we derive the conservation equations for properties (e.g. heat and a solute) across a double diffusive interface between two well-mixed layers. A nondimensional measure of the entrainment across an interface and the most suitable choice for the buoyancy flux ratio are presented. Some surprising facts emerge. First, even for a linear equation of state and in the absence of direct entrainment across the interface, the flux of water across a finger interface is shown to be important. Second, for the heat-solute system, the heat balance equations for each well-mixed layer contain terms proportional to the heat of solution of the solute and the partial specific enthalpy of pure water in a seawater solution. Third, the rate of change of gravitational potential energy of the two-layer system is shown to have several extra terms in addition to the two commonly quoted major terms.     

Nutrient attenuation in a shallow,gravel-bed river. II. Spatial and temporal changes in nitrogen dynamics and community metabolism

ABSTRACT

Instream processes alter the concentration and bioavailability of nutrients as they are transported downstream. By relating primary production and periphyton composition to changes in nutrient concentration in a gravel-bed river this study made inferences about recycling and attenuation. Where dissolved inorganic nitrogen (DIN) was abundant, concentrations decreased linearly with distance but by less than required to meet the nitrogen demand of primary production. Where DIN was barely measurable photosynthesis was reduced but only by 50%. We infer that recycling sustained primary production even when DIN concentrations were negligibly small. One implication is that DIN removal underestimates attenuation. Further experimental research on recycling and improved modelling is required to better quantify the length of streams adversely affected by nutrients.     

Effects of detailed soil spatial information on watershed modeling across different model scales

Hydro-ecological modelers often use spatial variation of soil information derived from conventional soil surveys in simulation of hydro-ecological processes over watersheds at mesoscale (10–100 km²). Conventional soil surveys are not designed to provide the same level of spatial detail as terrain and vegetation inputs derived from digital terrain analysis and remote sensing techniques. Soil property layers derived from conventional soil surveys are often incompatible with detailed terrain and remotely sensed data due to their difference in scales. The objective of this research is to examine the effect of scale incompatibility between soil information and the detailed digital terrain data and remotely sensed information by comparing simulations of watershed processes based on the conventional soil map and those simulations based on detailed soil information across different simulation scales. The detailed soil spatial information was derived using a GIS (geographical information system), expert knowledge, and fuzzy logic based predictive mapping approach (Soil Land Inference Model, SoLIM). The Regional Hydro-Ecological Simulation System (RHESSys) is used to simulate two watershed processes: net photosynthesis and stream flow. The difference between simulation based on the conventional soil map and that based on the detailed predictive soil map at a given simulation scale is perceived to be the effect of scale incompatibility between conventional soil data and the rest of the (more detailed) data layers at that scale. Two modeling approaches were taken in this study: the lumped parameter approach and the distributed parameter approach. The results over two small watersheds indicate that the effect does not necessarily always increase or decrease as the simulation scale becomes finer or coarser. For a given watershed there seems to be a fixed scale at which the effect is consistently low for the simulated processes with both the lumped parameter approach and the distributed parameter approach.     

Exploring the sensitivity of coastal inundation modelling to DEM vertical error

As sea level is projected to rise throughout the twenty-first century due to climate change, there is a need to ensure that sea level rise (SLR) models accurately and defensibly represent future flood inundation levels to allow for effective coastal zone management. Digital elevation models (DEMs) are integral to SLR modelling, but are subject to error, including in their vertical resolution. Error in DEMs leads to uncertainty in the output of SLR inundation models, which if not considered, may result in poor coastal management decisions. However, DEM error is not usually described in detail by DEM suppliers; commonly only the RMSE is reported. This research explores the impact of stated vertical error in delineating zones of inundation in two locations along the Devon, United Kingdom, coastline (Exe and Otter Estuaries). We explore the consequences of needing to make assumptions about the distribution of error in the absence of detailed error data using a 1 m, publically available composite DEM with a maximum RMSE of 0.15 m, typical of recent LiDAR-derived DEMs. We compare uncertainty using two methods (i) the NOAA inundation uncertainty mapping method which assumes a normal distribution of error and (ii) a hydrologically correct bathtub method where the DEM is uniformly perturbed between the upper and lower bounds of a 95% linear error in 500 Monte Carlo Simulations (HBM+MCS). The NOAA method produced a broader zone of uncertainty (an increase of 134.9% on the HBM+MCS method), which is particularly evident in the flatter topography of the upper estuaries. The HBM+MCS method generates a narrower band of uncertainty for these flatter areas, but very similar extents where shorelines are steeper. The differences in inundation extents produced by the methods relate to a number of underpinning assumptions, and particularly, how the stated RMSE is interpreted and used to represent error in a practical sense. Unlike the NOAA method, the HBM+MCS model is computationally intensive, depending on the areas under consideration and the number of iterations. We therefore used the HBM+ MCS method to derive a regression relationship between elevation and inundation probability for the Exe Estuary. We then apply this to the adjacent Otter Estuary and show that it can defensibly reproduce zones of inundation uncertainty, avoiding the computationally intensive step of the HBM+MCS. The equation-derived zone of uncertainty was 112.1% larger than the HBM+MCS method, compared to the NOAA method which produced an uncertain area 423.9% larger. Each approach has advantages and disadvantages and requires value judgements to be made. Their use underscores the need for transparency in assumptions and communications of outputs. We urge DEM publishers to move beyond provision of a generalised RMSE and provide more detailed estimates of spatial error and complete metadata, including locations of ground control points and associated land cover.     

Spatial Concentration in Australian Regional Development,Exogenous Shocks and Regional Demographic Outcomes: a South Australian case study

ABSTRACT

As a tribute to the massive contribution of our friend and colleague Graeme Hugo to the population and settlement geography of Australian rural areas, this paper presents a longitudinal study from his home State. It forms part of a wider study of the long-term demographic relationships between Australia’s rapidly growing regional cities and their surrounding functional regions. Of particular interest is the question of what effect the accelerating concentration of population and economic activity into a given regional city will have for the longer term demographic sustainability of its functional region as a whole. Taking the case of Port Lincoln, regional capital of most of South Australia’s Eyre Peninsula, it examines the nature of change in the functional region over the period 1947–2011, and investigates the forces feeding, and partly counteracting, the population concentration process, informed by concepts of evolutionary economic geography. In particular it traces the demographic impact (particularly differential migration and ageing trends) of exogenous shocks to the region’s essentially primary productive economic base during the period of major change from 1981 to 2011.     

Cordierite breakdown under high-pressure,hydrous conditions

Clear evidence exists for a cordierite breakdown reaction to amphibole-kyanite-quartz in high-grade metamorphic rocks of the Arunta Complex, Australia. Using the natural minerals this reaction has been duplicated experimentally. It proceeds over a divariant band with a slope of 12±4 bars/°C, occurring between 8 and 10.4 kb at 750° C and between 9.5 and 11.3 kb at 850°C. The reaction is cut off at low temperature by the appearance of talc and at high temperature by the appearance of orthopyroxene. The maximum pressure stability of the amphibole-kyanite-quartz assemblage is about 20 kb. These data suggest that the natural rock was subjected to pressures of at least 8 kb at 750–850° C for high water fugacities. Other experimental data on the hydration of hypersthene and cordierite-hypersthene stability, point to a temperature below 820° C and an upper pressure limit of 9.5 kb at 750–820°C. Experiments at \(P_{{\text{H}}_{\text{2}} {\text{O}}}\) total indicate that the breakdown of cordierite to amphibole-kyanite-quartz is a hydration reaction, and occurred in the natural rock as a result of an increase of water fugacity at constant total pressure (8–9.5 kb) and temperature (750–820°C).     

Experimental duplication of a high-pressure megacryst/cumulate assemblage in a near-saturated hawaiite

The occurrence of corroded megacrysts and cumulates of olivine, clinopyroxene, orthopyroxene, plagioclase, ilmenite and apatite in near-saturated hawaiites from the mid-north coast of New South Wales point to the derivation of these hawaiites at elevated pressures. In an experimental study on one of these hawaiites under conditions ranging from 5–15 kb and 0–5% H₂O, orthopyroxene was identified in only one run with 2% H₂O at 1040° C and 6.5 kb. In this run it was associated with olivine, clinopyroxene and Fe-Ti oxide. The early appearance of plagioclase in the “dry” experimental runs and amphibole in runs with 5% H₂O, indicates that the water content in the natural hawaiite was intermediate to these values. The near-duplication of the natural megacryst-cumulate assemblage suggests that the hawaiite host precipitated these phases at a depth of approximately 20–24 km, prior to rapid eruption to higher crustal levels.     

Pressure effect on Ti- or P-rich accessory mineral saturation in evolved granitic melts with differing K2O/Na2O ratios

The solubility of Ti- and P-rich accessory minerals has been examined as a function of pressure and K₂O/Na₂O ratio in two series of highly evolved silicate systems. These systems correspond to (a) alkaline, varying from alkaline to peralkaline with increasing K₂O/Na₂O ratio; and (b) strongly metaluminous (essentially trondhjemitic at the lowest K₂O/Na₂O ratio) and remaining metaluminous with increasing K₂O/Na₂O ratio (to 3). The experiments were conducted at a fixed temperature of 1000 °C, with water contents varying from 5 wt.% at low pressure (0.5 GPa), increasing through 5–10 wt.% at 1.5–2.5 GPa to 10 wt.% at 3.5 GPa. Pressure was extended outside the normal crustal range, so that the results may also be applied to derivation of hydrous silicic melts from subducted oceanic crust.

For the alkaline composition series, the TiO₂ content of the melt at Ti-rich mineral saturation decreases with increasing pressure but is unchanged with increasing K content (at fixed pressure). The P₂O₅ content of the alkaline melts at apatite saturation increases with increased pressure at 3.5 GPa only, but decreases with increasing K content (and peralkalinity). For the metaluminous composition series (termed as “trondhjemite-based series” (T series)), the TiO₂ content of the melt at Ti-rich mineral saturation decreases with increasing pressure and with increasing K content (at fixed pressure). The P₂O₅ content of the T series melts at apatite saturation is unchanged with increasing pressure, but decreases with increasing K content. The contrasting results for P and Ti saturation levels, as a function of pressure in both compositions, point to contrasting behaviour of Ti and P in the structure of evolved silicate melts. Ti content at Ti-rich mineral saturation is lower in the alkaline compared with the T series at 0.5 GPa, but is similar at higher pressures, whereas P content at apatite saturation is lower in the T series at all pressures studied. The results have application to A-type granite suites that are alkaline to peralkaline, and to I-type metaluminous suites that frequently exhibit differing K₂O/Na₂O ratios from one suite to another.